Problem: The following line passes through point $(5, 7)$ : $y = \dfrac{5}{2} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(5, 7)$ into the equation gives: $7 = \dfrac{5}{2} \cdot 5 + b$ $7 = \dfrac{25}{2} + b$ $b = 7 - \dfrac{25}{2}$ $b = -\dfrac{11}{2}$ Plugging in $-\dfrac{11}{2}$ for $b$, we get $y = \dfrac{5}{2} x - \dfrac{11}{2}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(5, 7)$